A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm {~m} ^ { 2 }$. If the speed of the air is $180 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ over the lower wing surface and $252 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ over the upper wing surface, the mass of the plane is $\_\_\_\_$ kg. (Take air density to be $1 \mathrm {~kg} \mathrm {~m} ^ { - 3 }$ and $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$)